Assessing similarities in “call repertoire” for animal vocalizations

Question

I have count data for number of call types over an interval of time for multiple animals. What I want is (1) a summary of association between call types (i.e., if X1 is large, X2 is small) and (2) a measure of similarity between the animals "repertoire" or rather pattern in which they call (comparison of correlation structure of animals' calls?). My data looks like the following:

Animal    Time    X1    X2    X3    X4    ...    Xn 
A            1    0      5     3     1    ...     0
A            2    5      1     1     8    ...     6
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C            1    3      3     5     1    ...     3
C            2    0      0     2     1    ...     5

Where X1, X2, ... Xn represent call type (i.e., 'Scream', "Howl', 'Laugh', etc). I'm not really sure where to start with this sort of data.

Answer 1

For (1), you may do a linear correlation between each pair of vocalizations. In R:

fit <- lm(X2~X1, data=your_data)
summary(fit)
fit <- lm(X3~X1, data=your_data)
summary(fit)
fit <- lm(X3~X2, data=your_data)
summary(fit)
...

For (2), the context is probably very important. All animals were seen together (e.g. in "time 1")? As a first approximation, you can try a multivariate analysis, excluding the column "Time". In R:

fit <- prcomp(your_data)
plot(fit$x)

Hope that helps!